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Ukrainian Mathematical Journal

, Volume 58, Issue 5, pp 794–797 | Cite as

On iteration stability of the Birkhoff center with respect to power 2

  • I. Yu. Vlasenko
  • E. O. Polulyakh
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Abstract

It is proved that the Birkhoff center of a homeomorphism on an arbitrary metric space coincides with the Birkhoff center of its power 2.

Keywords

American Mathematical Society Cycle Length Open Ball Ordinal Number Entire Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    E. Coven and Z. Nitecki, “Nonwandering sets of the powers of maps of the interval,” Ergod. Theory Dynam. Syst., 1, 9–31 (1981).zbMATHMathSciNetCrossRefGoogle Scholar
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    W. H. Gottschalk, “Powers of homeomorphisms with almost periodic properties,” Bull. Amer. Math. Soc., 50, 222–227 (1944).zbMATHMathSciNetCrossRefGoogle Scholar
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    C. Conley, Isolated Invariant Sets and the Morse Index, American Mathematical Society, Providence, RI (1978).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • I. Yu. Vlasenko
    • 1
  • E. O. Polulyakh
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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